burkhardt



Reissued Dec. 1, 1953 RAILWAY RAILHN Geor'gfe Ri Burkhardt,Qhica'gmilllc-u orig ating,lzszac'o datedecember 19's SerialiNo, 568309}December {151 1921 i cation 'forl reissuc January -.10-,- --1a52*,="sm19 Claimant: (Cl. 213M125) Matter enclosed inheavy brackets appears inthe: original pateht' but forms no part of this reissue specification;matterprinted in italics indicates the additions;madeby reissue. I

This case is a continuation part of my pending application?Serial"*N6f"*438,31l, now abandoned, Alled April. .9, 1942, and relates torailway railshf'tne' vignclestype, i. e.,' railswhich are ofsubstantially T-shape in cross-section, and has particular reference toan improved distribution of metal in suchrailsji for the purpose ofreducing stress :concentrations therein,particularly'iinllan'd.aboutiithe head-web and base 'we'b filltsitliereoiiwhre;"according to" prior rail 'de' signs,"undesirablehighand'dangerous stress con: centrations have occurred.

Stress concentration .in.. and-about the headweb and the bases-web'fill'etsof T-raiis causes fatigueioftmetaltin theselocationsand. areconducivetousplit heads; crackedtwebs, and-other types of rail failures.In this connection, the A. R. E. A. formulae forstresses in railwayrails (page 886, A. R. E. A.,- volume 19) are based on the assumptionthat the stress is distributed acq cordingi to" the law that. it"increasesuirectly as the" distance'from the neutral axis? However theabrupt ""ch'angesoccurring in T-iail sections results in discontinuityin the distribution of stress. Accordingly, thsaid A. R. E. A. formulaefor calculating stress in rails is, in many cases, not'everraroughiapproxi-matiomofcthermaximumszstress concentrated in the head-weband the. base welri filletstzof fa fidyriamically'aloaded? sraila' Inethr wordsj rail design practi'cesit heretofore no in rogue -do not take-'into considerationz tall 'ofc. f thei-factors esserrtial tor-reductionin stress 56011-1115 cent/ration in andab out-the" mau aw eb :andx:thex.base web' fill 'tsof T-iail ln thair theyi do not sufilclentl y'consi'dei the relationship of the' di trihiiti'on ofmetal in the web atits junction: wi 1 the head and' th baise of the rail as well as therelation' of th v width an'd depthof the: head tom the'wwidth of the--web-: These facts tea'ch I-tlie'; necessity of a -more fundamental'study Poi the' Je; 0 stress conditions in th unctu'resof.=head andwebs-and web'with basei- Toi'thisien'd', extensivec; studies have been.'::made kWhiCl-T would establish the effect of -proportions". off thehead; web and o fillets *of tlfe =rai1-*section 'on theresultingxstress:5 concentrations. The study ofthefiect of 'theseproportions was made from the measurements ofstrains in the rail asshown by two 'dimensional photoelastic and strain gage tests on railsand from membrane analogy-n Tests were made on 5 models with verticalloads applied accentrically to the heads 'Ihe ibasecofethetrailwasiuniformly supporteddnisome cases. and in other; cases-the .l, base'twas supported-xonly zatathe s edges to simulate the conditionsresultingairclmzthe 11S'11a1fCOI16a7l/e'r5 tiecplatera Investigatic'mwasmade of :the stress-o in modtels- -imwhich thei-rat-iofidepth offlangeto: widtlik ofwwebawas-ikeptrcconstant and 'the ratios of width of 'ihead towidth :offweb; and ratio= of- "radiuszof zfillet toawidth of Webvaried;-1.Investi-.

gationwasalsmmadewo-f theeffect of 'de'ep flanges;

Therefore,-i.-tlre1-:primary ,objectof the" presentsinventionis toiprovideia :T-rail having an ecor1om-ica'hand-eiiicientmetalidistriloution:involvingcf a novel ratio..ofvwidtlr-iofweb at the j-unctiomofw thefheadawebz-and theibase'eweb filletstherewith to the radii fzs'aid.lhead-.-web: andsbaser-web fillets, i:combinedwith:v a widtlfiand depth of -zthe -he'ad-,..- suchzthatihiglrand "dangerous stress-concentrate; tions inland? about-.sthehead-webandthe -:base#- wetx==fillets-;.andr throughout: the -rai1v areavoided-.2, That is iato say,:.- whilethe stressv concentration t;factor. s the ratioibetween-the stress in the filletsmiths-stress'iin'sitlie =web, ithis: factor :in a shape such as a rail,where the change in shape from iwebito h'adiand web :toibasei's rapid;-is -a simul taneous function; of 'th'erratio width and depth of i head=ton width' ofrwveb combined with "a novel radius lofi fillet toW'i'dthi-Of webvratio;tandthesem ratiosli are'" criticali'im mutually-producing a safe and emcientnraih:

According :totethei present -invention; the -radiic of 'the'head-webifilletsz are "substantially. equ'a1;-:t0= theiwidth ofithewebi-rattheljuncture oftthe headwand thel-webzlii Imother words; theheadoven-fillets of a railxprodu'cedrih accordance with the presentinventionvhaveiconsiderably longer-radii thant-he head'eweblfill'etsof'lra'ils producedin accordance with prior practice. As a consequence,wide bearaing'ar-eas are afforded to be engaged =by :the heads widebearing areas-are conducive toii'oiigerclife' and"mOresatisfaEtOr-y"performance generally J of v, He'adfre-j oints if thelatter areemployedtozconuf. .nectthepresentrails. Tlius; rails produce'dinaccorda'nce'with-"the"- presentinvention are specially adapted foradvantageous connection-by- Hea'dfr'e'e' joints:

With the foregoingandother objectsin view?"- .wh'lch will more'readily'appear-to those familiar withth'e art; as the-"intention "isbetter under stood',."the same consists in-the novel metal distributioii" and proportion of" parts herei'naftr more fully described;"illustrated-in the -ac'com*-=- panyingdrawings, and defined in theappended claims.

In the accompanyingdrawings: Figure 1 is an end elevation of a rail, infull lines-,5: having tits. -metal distributed. inaccord-.. ance' withthe present'mventionwhile the-.- bro--- ken lines show the distortionresulting from loading the rail in the manner described.

Figure 2 is a chart showing a series of graphs indicating the results ofstudies of different rail sections, and teaches the ideal ratios betweenradius of fillets and the width of web and ratios of width of head towidth of web at the juncture with the fillets.

Referring to the drawings in detail, it will be observed from Figure 1that the present rail is of the Vignoles or T-type and comprises, asusual, a head I, web 2, base 3 and head-web and baseweb fillets 4 and 5,respectively, at the junctures of the head and the base with the web.Also, dimension lines with reference letters are shown to describe theideal proportionof the metal distribution of the present invention.

Generally the letter C has been used to designate the width of flanges,treating the head I as well as the base 3 as such, and likewise R and Uare used in the equations to designate the radii of the fillets andwidth of web at the juncture of the fillets therewith respectively, sothat the graphs of Fig. 2 will apply equally to the head or the base andM generally designates the depth of the flanges. However, as will beseen from the drawing, an appropriate subscript is used in each case todesignate the specific flange, radius or web thickness. For example, CHdesignates the width of the head and CB designates the width of thebase, while the radii of the head fillets 4 and base fillets 5 arerespectively designated as RH and RB, and the width of the web 2 at thejunction of said fillets with the web is also respectively designated asUH and UB. The depth of the head I is indicated as Mn and the depth ofthe base is shown by the reference MB. Also the width of the head alongthe top line of the fishing is designated as CF.

The outer sides of the web 2 are each of a substantially flat concavecurvature as conventional in rails of the Vignoles type and the point ofminimum thickness of the web is between the head fillets and basefillets along a horizontal line passing through the center of curvatureof the arcs. of greatest radii of the web on opposite sides of thevertical center line of the cross section of the rail. For example, inFig. '1, the dimension T represents the minimum, width of the web,andthe dimensions UH and U represent the maximum width of the web. The

ratio of T to overall rail heights is empirically determined.

As previously indicated, the present invention relates to a newdistribution of metal in the web, head and base of the rail where thefactors to be considered arethe relationship of the width and depth ofthe head to the. width of the web and the radii of the fillets to widthof web. The graphs-show that these ratios simultaneously 'affeet thestress concentration factor.

Referring first to the feature 'of'the radii of the fillets 4 and 5joining the web 2 to the head I and the web 2 to the base 3 of therailand assuming, for example, that RH and R13 are the radii of the fillets,andUH and Us are respectively the thickness of the web at the junctionwith the head and base fillets, it has been found that stressconcentration in said fillets increases with decrease of the ratio belowone or unity and also increases again with increase of said ratio aboveone or. unity. In.

other words, it has been found that stress concentration in said filletsdecreases rapidly to a minimum when and that R R fi-0.8 and I are thedesirable limits to be placed on this ratio. The ratio of is madebecause the stress concentration factor is lowest'at this point. Thegraphs show a substantial equality in the stress concentration factorbetween the ratio R R R fi-(LS, and It is to be noted that there is asharp increase in the stress concentration factor for the ratio In otherwords, 0.8 is just below the knee of the curve which is substantiallyhorizontal between 0.8 and 1.6. At the point where the ratio of thecurves again turn upward at an increasedrate.

Referring now to the width CH of thehead I I and the width of the baseCa in relation to the Width UH or Us of the web and the radii RH and RBof the fillets, my studies of rail stress by membrane analogy show thatstress concentration increases rapidly when the ratio of width of head Cto width U of web exceeds four, and likewise stress concentrationincreases again when thewidth C of the head is less than two andone-half times the width U of the web tion which is not less than twicethe width C of the head section I.

In Figure 2 The line-marked.

contains points obtained by investigating? the old type rails, forexample, the A. R. E. A. 112.1b. sections and modifications thereof suchas ducing the width of the head.

5 v 'Ilie-dottd -linE- marked :11

-2.4 and- OJ shows thei efieet of 'sincreasingzthe ratio of radius ofhead-web fillet to width ofrwehxandemain q taming-the sameiratio iof.depthfuof hadctowidth of-web foundzixrthe firstrlines.

The line marked and 2-:-

P vREL. V

wasldr-awn throughv points obtained front-measurements tofu. railsstrained as; shown -in=--Fig. v 1 a The.=.line marked -Mand l -1.0..

shows that: lowest stress -:.concentration= factors result Arom equalityi-betweem the thickness. lof:

The lline :marked; a

. 1; ,-4.0 and 1.0.

15 substantially horizontalsbecause the bending J30 ofithe fianges isnegligiblewhen Myianalysisof stressin 'railwayrail with curved websshoWsthatthe shearing 'stressin'theweb increases" in'verse1y'"as the:radius of the curves.

Alsoj'when a fillet"'ra'diusiis'employed equal to. the width of webatthe" point bf .1 compounding; stress concentration is a minimum?Furthermore," my' analysis demonstrates thatthe transition of the stressfrom web to head is'lesscritical when the radius of the filletiequalsthewidth'of the web.

My experience with failed rails, particularly failureinth'e base, showsthat concave tieplates and "convex rail bases cause'xthe type ofbend-t." in'g'in the baseshowninF'lgure' l. Accr'dingly', g itisimportant" that the'radiusof the" fillet as; is inot'less'than 0.8 times'thedepthof the. baseat the juncture or point of .tang'ency with thefillet Also "the radius ofIfilletshould not be more than 1.6 times the"depth ofxbase. The. idealratio is of course"'1.0 so"that* ati'the pointof ta'ngency'with' fillet the Width of web should 5 equal the depth ofbase;

Thus, the graphs of Figure'2 teachth'e ideal ratios between radius offilletsand' the width of'web and ratio of. width'of head tonwidth 'ofweb of'the juncture with the fillet. Therseveral J illustrations" givendefinitely show that thesev ratios simultaneouslvafiect the stressconcentrationfactor; The maximum. stress; a max, occurring'in the filletjoininghead and web and web and base "can be expressed as" a multiple")of thenominal stress; a nom, in the web; Thus. a maxzkv' nom' where'kisthe stress concentration factor.

The studies" undertaken showed that the following ,factors contribute toan increase in the max stress, .1 max.

With respect to the relation. ofithe point of load tofllletsyi. e.,'theratio of widthof flange to-width'of web, as shown "in the graphs, thestraight edge'of' the'cross section opposite the 6 t filletr'esul-ts-"in a slight ihcre'ase-imth stressseem-kw centration factor,when The ratio the web -at the juncture ofthehead-webnllets V therewithas illustrated byVU Hf Thusyaccordin'g to'th'e drawingpthelowest limitof the .ratio":

this bending-canbe :disreg'arded.= The'zstress con-a centration, then;increases asthratio M1; U decreasesfassumings that:

iskeptconstant. v

The solid line's' in the graph were drawnwhene; three :1011 imore.pointswwere lo'bt'ainedwfrom test-i data. The-dotted. lines-were drawnwhen only:;; 011E501 tWOnpQiIltS could. be obtained-:from testa data; 4.The rSOlidvdOliS indicate: points confirmed 1* by; photoelastiouexhibits. :v The =:open- .;dots=. indie;

cate; r/points obtained: from test 'ameasurments-s The numerals assignedto thel'points are: the ;-test or: :exhibitrnumbers-at Points RA H 5:is. the: cr sulti'ofs tests on::a railthaving'tthe following pro-1portionsi 1 as V. ca

Tests have [been] shown that theshapesof-the-- 'curvesor'graphs aresimilar when" the stress I concentration factor is platted as a functionof the ratios coupled with C H C B UH and E; The most economical andsatisfactory metal distribution results from making not less than 0.8nor more than 1.6 and at the same time making and not more than 4.0

As to the feature of providing increased bearing area between theunderside of a Headfree rail at the location of the fillets 4 and thetop bearing surface of a Headfree joint bar, it may be pointed out thatin the Headfree type rail, the width of the head at the top of thefishing may be defined in terms of the width of the web at the juncturewith the head-web fillets. If R=U then the width Cr' of the head alongthe top line of the fishing equals ture, the point of minimum width ofsaid web lying between the point of tangency of the headweb and base-webfillets with the web and being along a horizontal line passing throughthe center of curvature of the arcs of greatest radii of the web onopposite sides of the vertical center line of the cross section of therail, the width of the web at the juncture with the head-web andbase-web fillets being not less than said minimum width, the radius ofeach of said fillets being not more than 1.6 and not less than 0.8 timesthe width of the web at its juncture with the fillets, said head sectionat its thickest point having a depth of not more than 4 and not lessthan 2.4 times the width of the web at the juncture of web and head-webfillets, the maximum width of said head being not more than 4 times andnot less than 2.5 times the width of the web at the juncture of the weband head-web fillets, the overall height of the rail being not more than13 times the minimum width of web, not more than 1%, times and not lessthan the width of the base to provide against overturning by theresultant of vertical and lateral loads and being greater than the widthof the base section which is not less than twice the width of the headsection.

2. A Vignoles type rail according to claim 1 wherein the radii of thefillets are equal to the width of the web at the point of tangency ofsaid fillets with said web.

3. A Vignoles type rail construction according to claim 1 wherein thedepth of the base section at the point of tangency of the base-webfillets therewith is not less than 0.8 or more than 1.6 times the radiusof the base-web fillets.

4. A Vignoles type rail construction according to claim 1 wherein thedepth of the base at the point of tangency of the base-web filletstherewith is equal to the radius of the base-web fillets.

5. A Vignoles type rail having a head section, a base section, a websection, head-web fillets and base-web fillets, the sides of said websection being of a substantially flat concave curvature, the point ofminimum width of said web lying between the point of tangency of thehead-web and base-web fillets with the web and being along a horizontalline passing through the center of curvature of the arcs of greatestradii of the web on opposite sides of the vertical center line of thecross section of the rail, the width of the web at the juncture with thehead-web and base-web fillets being not less than said minimum width,the radius of each of said fillets being not more than 1.6 and not lessthan 0.8 times the width of the web at its juncture with the fillets,said head section at its thickest point having a depth of not more than4 and not less than 2.0 times the width of the web at the juncture ofweb and head-web fillets, the maximum width of said head being not morethan 4 times and not less than 2.5 times the width of the web at thejuncture of the web and headweb fillets.

6. A Vignoles type rail having a head section, a base section, a websection, head-web fillets and base-web fillets, the sides of said websection being of a substantially flat concave curvature, the point ofminimum width of said web lying between the point of tangency of theheadweb and base-web fillets with the web and being along a horizontalline passing through the center of curvature of the arcs of greatestradii of the web on opposite sides of the vertical center line of thecross section of the rail, the width of the web at the juncture with thehead-web and base-web fillets being not less than said minimum width,the radius (of each) of said head-web fillets being not more than 1.6and not less than 0.8 times the width of the web at its juncture withthe head-web fillets, the depth of the base section at the point oftangency of the base-web fillets therewith being not less than 0.8 ormore than 1.6 times the radius of the base-web fillets, and said headsection at its thickest point having a depth of not more than 4 and notless than 2.0 times t e width of the web at the juncture of web andhead-web fillets, the maximum width of said head being not more than 4times and not less than 2.5 times the width of the web at the junctureof the web and head-web fillets.

7. A Vignoles type rail having a head section, a base section, a websection, head-web fillets and base-web fillets, the sides of said websection being of a substantially flat concave curvature, the point ofminimum width of said web lying between the point of tangency of theheadweb and base-web fillets with the web and being along a horizontalline passing through the center' of curvature of the arcs of greatestradii of the web on opposite sides of the vertical center line of thecross section of the rail, the width of the web at the juncture with thehead-web (and base-web) fillets being not less than said minimum width,the radius (of each) of said fillets being not more than 1.6 and notless than 0.8 times the width of the web at its juncture with thefillets, said head section at its thickest point having a depth of notmore than 4 and not less than 2.0 times the width of the web at thejuncture of web and head-web fillets, the maximum width of said headbeing not more than 4 times and not less than 2.5 times the width of theweb at the juncture of the web and headweb fillets, the width of the webat the juncture with the base-web fillets being not less than saidminimum width, the of the base-web fillets being not more than 0.3 andnot less than 0.5 times the width of the web at the juncture with saidbase-web fillets.

8. A Vignoles type rail having a head section, a base section, a websection, head-web fillets and base-web fillets, the sides of said websection being of a substantially flat concave curvature, the point ofminimum width of said web lying between the point of tangency of theheadweb and base-web fillets with the web and being along a horizontalline passing through the center of curvature of the arcs of greatestradii of the web on opposite sides of the vertical center line of thecross section of the rail, the width of the web at the juncture with thehead-web and base-web fillets being not less than said than 4 and notless than 2.0 times the width of the web at the juncture of web andhead-web fillets, the maximum width of said head being not more than 4times and not less than 2.5 times the width of the web at the junctureof the web and head-web fillets, the width of the web at the juncturewith the base-web fillets being not less than said minimum width, theradii of the base-web fillets being not more than 0.8 and not less than0.5 times the width of the web at the juncture with said base-webfillets.

9. A Vignoles type rail having a head section, a base section, a websection, head-web fillets and base-web fillets, the sides of said websection being of a substantially fiat concave curvature, the point ofminimum width of said web lying between the point of tangency of theheadweb and base-web fillets with the web and being along a horizontalline passing through the center of curvature of the arcs of greatestradii of the web on omiosite sides of the vertical center line of thecross section of the rail, the width of the web at the juncture with thehead-web (and base-web) fillets being not less than said minimum width,the radius (of each) of said fillets being substantially equal to thewidth of the web at its juncture with the fillets, said head section atits thickest point having a depth of not more than 4 and not less than2.0 times the width of the web at the juncture of web and head-webfillets, the maximum width of said head being not more than 4 times andnot less than 2.5 times the width of the web at the juncture of the weband head-webfillets, the width of the web of the juncture with thebaseweb fillets being not less than said minimum width, the radii of thebase-web fillets being not more than 0.8 and not less than 0.5 times thewidth 0 the web at the juncture with. said base-web fillets.

GEORGE R. BURKHARDT.

References Cited in the file of this patent or the original patentUNITED STATES PATENTS Number Name Date 2,260,211 Burkhardt Oct. 21, 1941FOREIGN PATENTS N umber Country Date 1,856 Great Britain May 29, 1875()TI-IER REFERENCES Stress Concentration Produced by Holes and Fillets,by S. Timoshenko and W. Dietz, American Society Mechanical Engineers,Transactions 1925, page 212, section et seq.

Torsion in Structural Beams, by F. L. Ehasz, Lawrence Calvin Brink,Research Fellow in Civil Engineering, Lehigh University.

Railway Age, December 12, 1942, pp. 953-967, vol. 113, No. 24.

Steel Rails, by William Sellew. Plate No. XVII, deposited in the U. S.Patent Ofiice Library June 26, 1941, printed in 1913 by Van Nostrang Co.of New York.

